Atkin-Lehner |
5+ 7+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
89425b |
Isogeny class |
Conductor |
89425 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
306432 |
Modular degree for the optimal curve |
Δ |
-164386903515625 = -1 · 58 · 78 · 73 |
Discriminant |
Eigenvalues |
-1 0 5+ 7+ -5 -2 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-54130,-4872878] |
[a1,a2,a3,a4,a6] |
Generators |
[284:1470:1] [409:6220:1] |
Generators of the group modulo torsion |
j |
-194726889/1825 |
j-invariant |
L |
6.0835663558078 |
L(r)(E,1)/r! |
Ω |
0.15641121873017 |
Real period |
R |
19.447346568799 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000032 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17885a1 89425l1 |
Quadratic twists by: 5 -7 |